Disordered Crystals from First Principles I: Quantifying the Configuration Space

TL;DR

This paper develops a first-principles method to quantify the configuration space of disordered crystals, exemplified on silicon, enabling accurate generation of thermally-disordered atomic configurations for electronic transport simulations.

Contribution

It introduces an algorithmic approach to characterize the configuration space and Gibbs measure of disordered crystals from first principles, demonstrated on silicon.

Findings

Gibbs measure is well approximated by a multivariate normal distribution.

Parameters of the distribution are temperature-dependent and tabulated.

Generated configurations can be used for electronic transport simulations.

Abstract

This work represents the first chapter of a project on the foundations of first-principle calculations of the electron transport in crystals at finite temperatures. We are interested in the range of temperatures, where most electronic components operate, that is, room temperature and above. The aim is a predictive first-principle formalism that combines ab-initio molecular dynamics and a finite-temperature Kubo-formula for homogeneous thermodynamic phases. The input for this formula is the ergodic dynamical system $(\Omega,\mathbb G,{\rm d}\mathbb P)$ defining the crystalline phase, where $\Omega$ is the configuration space for the atomic degrees of freedom, $\mathbb G$ is the space group acting on $\Omega$ and ${\rm d}\mathbb P$ is the ergodic Gibbs measure relative to the $\mathbb G$-action. The present work develops an algorithmic method for quantifying $(\Omega,\mathbb G,{\rm d}\mathbb P)$ from first principles. Using the silicon crystal as a working example, we find the Gibbs measure to be extremely well characterized by a multivariate normal distribution, which can be quantified using a small number of parameters. The latter are computed at various temperatures and communicated in the form of a table. Using this table, one can generate large and accurate thermally-disordered atomic configurations to serve, for example, as input for subsequent simulations of the electronic degrees of freedom.